Question

$K_P$ for the reaction $N_2+{3H}_2\rightleftharpoons {2NH}_3$ at 400C is $1.64\times {10}^{-4}$. Find $K_C$. Also find ${△G}^{\oplus }$ using $K_P$ and $K_C$ values and interpret the differences.

• A. $K_C=0.025$
  ${△G}^{\oplus }=+11.733kcal$
• B. $K_C=2.001$
  ${△G}^{\oplus }=+19.249kcal$
• C. $K_C=0.5006$
  ${△G}^{\oplus }=+11.733kcal$
• D. $K_C=1.5$
  ${△G}^{\oplus }=+15.22kcal$

Answer 1

The correct option is C $K_C=0.5006$

${△G}^{\oplus }=+11.733kcal$

$\Delta n=2-[1+3]=-2$

$K_p=K_c(RT{)}^{\Delta n}$

$1.64\times {10}^{-4}=K_c(0.08206\times 673{)}^{-2}$

$K_c=0.5006$

$\Delta G^0=-RTln{K}_p=-2\times 673\times ln1.64\times {10}^{-4}=11731cal/mol=11.733kcal/mol$

$\Delta G^0=-RTln{K}_c=-2\times 673\times ln0.5006=932cal/mol=0.93kcal/mol$

The standard free energy change calculated form $K_p$ is higher than the standard free energy change calculated from $K_c$ as the numerical value of $K_c$ is higher than the numerical value of $K_p$